Problem Statement: Let $D$ be a directed graph with average (total) degree $d(D)\ge 16$. Prove that there is a cycle in $D$ containing no directed path of length 2.
I'm not sure how to begin with this one. The only concept I've learned involving directed graphs is Gallai and Milgram's Theorem that every directed graph has path cover $\mathcal{P}$ and an independent set of vertices $\{v_P \mid P \in \mathcal{P}\}$ s.t. $v_P \in P$ for every $P \in \mathcal{P}$, but I can't see a connection here. Any hints on how to start would be appreciated.